| /* This Source Code Form is subject to the terms of the Mozilla Public |
| * License, v. 2.0. If a copy of the MPL was not distributed with this |
| * file, You can obtain one at http://mozilla.org/MPL/2.0/. */ |
| |
| #include "mpi.h" |
| #include "mplogic.h" |
| #include "ecl.h" |
| #include "ecl-priv.h" |
| #include <stdlib.h> |
| |
| /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k * P(x, |
| * y). If x, y = NULL, then P is assumed to be the generator (base point) |
| * of the group of points on the elliptic curve. Input and output values |
| * are assumed to be NOT field-encoded. */ |
| mp_err |
| ECPoint_mul(const ECGroup *group, const mp_int *k, const mp_int *px, |
| const mp_int *py, mp_int *rx, mp_int *ry) |
| { |
| mp_err res = MP_OKAY; |
| mp_int kt; |
| |
| ARGCHK((k != NULL) && (group != NULL), MP_BADARG); |
| MP_DIGITS(&kt) = 0; |
| |
| /* want scalar to be less than or equal to group order */ |
| if (mp_cmp(k, &group->order) > 0) { |
| MP_CHECKOK(mp_init(&kt)); |
| MP_CHECKOK(mp_mod(k, &group->order, &kt)); |
| } else { |
| MP_SIGN(&kt) = MP_ZPOS; |
| MP_USED(&kt) = MP_USED(k); |
| MP_ALLOC(&kt) = MP_ALLOC(k); |
| MP_DIGITS(&kt) = MP_DIGITS(k); |
| } |
| |
| if ((px == NULL) || (py == NULL)) { |
| if (group->base_point_mul) { |
| MP_CHECKOK(group->base_point_mul(&kt, rx, ry, group)); |
| } else { |
| MP_CHECKOK(group->point_mul(&kt, &group->genx, &group->geny, rx, ry, |
| group)); |
| } |
| } else { |
| if (group->meth->field_enc) { |
| MP_CHECKOK(group->meth->field_enc(px, rx, group->meth)); |
| MP_CHECKOK(group->meth->field_enc(py, ry, group->meth)); |
| MP_CHECKOK(group->point_mul(&kt, rx, ry, rx, ry, group)); |
| } else { |
| MP_CHECKOK(group->point_mul(&kt, px, py, rx, ry, group)); |
| } |
| } |
| if (group->meth->field_dec) { |
| MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); |
| MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); |
| } |
| |
| CLEANUP: |
| if (MP_DIGITS(&kt) != MP_DIGITS(k)) { |
| mp_clear(&kt); |
| } |
| return res; |
| } |
| |
| /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + |
| * k2 * P(x, y), where G is the generator (base point) of the group of |
| * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. |
| * Input and output values are assumed to be NOT field-encoded. */ |
| mp_err |
| ec_pts_mul_basic(const mp_int *k1, const mp_int *k2, const mp_int *px, |
| const mp_int *py, mp_int *rx, mp_int *ry, |
| const ECGroup *group) |
| { |
| mp_err res = MP_OKAY; |
| mp_int sx, sy; |
| |
| ARGCHK(group != NULL, MP_BADARG); |
| ARGCHK(!((k1 == NULL) && ((k2 == NULL) || (px == NULL) || (py == NULL))), MP_BADARG); |
| |
| /* if some arguments are not defined used ECPoint_mul */ |
| if (k1 == NULL) { |
| return ECPoint_mul(group, k2, px, py, rx, ry); |
| } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { |
| return ECPoint_mul(group, k1, NULL, NULL, rx, ry); |
| } |
| |
| MP_DIGITS(&sx) = 0; |
| MP_DIGITS(&sy) = 0; |
| MP_CHECKOK(mp_init(&sx)); |
| MP_CHECKOK(mp_init(&sy)); |
| |
| MP_CHECKOK(ECPoint_mul(group, k1, NULL, NULL, &sx, &sy)); |
| MP_CHECKOK(ECPoint_mul(group, k2, px, py, rx, ry)); |
| |
| if (group->meth->field_enc) { |
| MP_CHECKOK(group->meth->field_enc(&sx, &sx, group->meth)); |
| MP_CHECKOK(group->meth->field_enc(&sy, &sy, group->meth)); |
| MP_CHECKOK(group->meth->field_enc(rx, rx, group->meth)); |
| MP_CHECKOK(group->meth->field_enc(ry, ry, group->meth)); |
| } |
| |
| MP_CHECKOK(group->point_add(&sx, &sy, rx, ry, rx, ry, group)); |
| |
| if (group->meth->field_dec) { |
| MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); |
| MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); |
| } |
| |
| CLEANUP: |
| mp_clear(&sx); |
| mp_clear(&sy); |
| return res; |
| } |
| |
| /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + |
| * k2 * P(x, y), where G is the generator (base point) of the group of |
| * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. |
| * Input and output values are assumed to be NOT field-encoded. Uses |
| * algorithm 15 (simultaneous multiple point multiplication) from Brown, |
| * Hankerson, Lopez, Menezes. Software Implementation of the NIST |
| * Elliptic Curves over Prime Fields. */ |
| mp_err |
| ec_pts_mul_simul_w2(const mp_int *k1, const mp_int *k2, const mp_int *px, |
| const mp_int *py, mp_int *rx, mp_int *ry, |
| const ECGroup *group) |
| { |
| mp_err res = MP_OKAY; |
| mp_int precomp[4][4][2]; |
| const mp_int *a, *b; |
| unsigned int i, j; |
| int ai, bi, d; |
| |
| ARGCHK(group != NULL, MP_BADARG); |
| ARGCHK(!((k1 == NULL) && ((k2 == NULL) || (px == NULL) || (py == NULL))), MP_BADARG); |
| |
| /* if some arguments are not defined used ECPoint_mul */ |
| if (k1 == NULL) { |
| return ECPoint_mul(group, k2, px, py, rx, ry); |
| } else if ((k2 == NULL) || (px == NULL) || (py == NULL)) { |
| return ECPoint_mul(group, k1, NULL, NULL, rx, ry); |
| } |
| |
| /* initialize precomputation table */ |
| for (i = 0; i < 4; i++) { |
| for (j = 0; j < 4; j++) { |
| MP_DIGITS(&precomp[i][j][0]) = 0; |
| MP_DIGITS(&precomp[i][j][1]) = 0; |
| } |
| } |
| for (i = 0; i < 4; i++) { |
| for (j = 0; j < 4; j++) { |
| MP_CHECKOK(mp_init_size(&precomp[i][j][0], |
| ECL_MAX_FIELD_SIZE_DIGITS)); |
| MP_CHECKOK(mp_init_size(&precomp[i][j][1], |
| ECL_MAX_FIELD_SIZE_DIGITS)); |
| } |
| } |
| |
| /* fill precomputation table */ |
| /* assign {k1, k2} = {a, b} such that len(a) >= len(b) */ |
| if (mpl_significant_bits(k1) < mpl_significant_bits(k2)) { |
| a = k2; |
| b = k1; |
| if (group->meth->field_enc) { |
| MP_CHECKOK(group->meth->field_enc(px, &precomp[1][0][0], group->meth)); |
| MP_CHECKOK(group->meth->field_enc(py, &precomp[1][0][1], group->meth)); |
| } else { |
| MP_CHECKOK(mp_copy(px, &precomp[1][0][0])); |
| MP_CHECKOK(mp_copy(py, &precomp[1][0][1])); |
| } |
| MP_CHECKOK(mp_copy(&group->genx, &precomp[0][1][0])); |
| MP_CHECKOK(mp_copy(&group->geny, &precomp[0][1][1])); |
| } else { |
| a = k1; |
| b = k2; |
| MP_CHECKOK(mp_copy(&group->genx, &precomp[1][0][0])); |
| MP_CHECKOK(mp_copy(&group->geny, &precomp[1][0][1])); |
| if (group->meth->field_enc) { |
| MP_CHECKOK(group->meth->field_enc(px, &precomp[0][1][0], group->meth)); |
| MP_CHECKOK(group->meth->field_enc(py, &precomp[0][1][1], group->meth)); |
| } else { |
| MP_CHECKOK(mp_copy(px, &precomp[0][1][0])); |
| MP_CHECKOK(mp_copy(py, &precomp[0][1][1])); |
| } |
| } |
| /* precompute [*][0][*] */ |
| mp_zero(&precomp[0][0][0]); |
| mp_zero(&precomp[0][0][1]); |
| MP_CHECKOK(group->point_dbl(&precomp[1][0][0], &precomp[1][0][1], |
| &precomp[2][0][0], &precomp[2][0][1], group)); |
| MP_CHECKOK(group->point_add(&precomp[1][0][0], &precomp[1][0][1], |
| &precomp[2][0][0], &precomp[2][0][1], |
| &precomp[3][0][0], &precomp[3][0][1], group)); |
| /* precompute [*][1][*] */ |
| for (i = 1; i < 4; i++) { |
| MP_CHECKOK(group->point_add(&precomp[0][1][0], &precomp[0][1][1], |
| &precomp[i][0][0], &precomp[i][0][1], |
| &precomp[i][1][0], &precomp[i][1][1], group)); |
| } |
| /* precompute [*][2][*] */ |
| MP_CHECKOK(group->point_dbl(&precomp[0][1][0], &precomp[0][1][1], |
| &precomp[0][2][0], &precomp[0][2][1], group)); |
| for (i = 1; i < 4; i++) { |
| MP_CHECKOK(group->point_add(&precomp[0][2][0], &precomp[0][2][1], |
| &precomp[i][0][0], &precomp[i][0][1], |
| &precomp[i][2][0], &precomp[i][2][1], group)); |
| } |
| /* precompute [*][3][*] */ |
| MP_CHECKOK(group->point_add(&precomp[0][1][0], &precomp[0][1][1], |
| &precomp[0][2][0], &precomp[0][2][1], |
| &precomp[0][3][0], &precomp[0][3][1], group)); |
| for (i = 1; i < 4; i++) { |
| MP_CHECKOK(group->point_add(&precomp[0][3][0], &precomp[0][3][1], |
| &precomp[i][0][0], &precomp[i][0][1], |
| &precomp[i][3][0], &precomp[i][3][1], group)); |
| } |
| |
| d = (mpl_significant_bits(a) + 1) / 2; |
| |
| /* R = inf */ |
| mp_zero(rx); |
| mp_zero(ry); |
| |
| for (i = d; i-- > 0;) { |
| ai = MP_GET_BIT(a, 2 * i + 1); |
| ai <<= 1; |
| ai |= MP_GET_BIT(a, 2 * i); |
| bi = MP_GET_BIT(b, 2 * i + 1); |
| bi <<= 1; |
| bi |= MP_GET_BIT(b, 2 * i); |
| /* R = 2^2 * R */ |
| MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group)); |
| MP_CHECKOK(group->point_dbl(rx, ry, rx, ry, group)); |
| /* R = R + (ai * A + bi * B) */ |
| MP_CHECKOK(group->point_add(rx, ry, &precomp[ai][bi][0], |
| &precomp[ai][bi][1], rx, ry, group)); |
| } |
| |
| if (group->meth->field_dec) { |
| MP_CHECKOK(group->meth->field_dec(rx, rx, group->meth)); |
| MP_CHECKOK(group->meth->field_dec(ry, ry, group->meth)); |
| } |
| |
| CLEANUP: |
| for (i = 0; i < 4; i++) { |
| for (j = 0; j < 4; j++) { |
| mp_clear(&precomp[i][j][0]); |
| mp_clear(&precomp[i][j][1]); |
| } |
| } |
| return res; |
| } |
| |
| /* Elliptic curve scalar-point multiplication. Computes R(x, y) = k1 * G + |
| * k2 * P(x, y), where G is the generator (base point) of the group of |
| * points on the elliptic curve. Allows k1 = NULL or { k2, P } = NULL. |
| * Input and output values are assumed to be NOT field-encoded. */ |
| mp_err |
| ECPoints_mul(const ECGroup *group, const mp_int *k1, const mp_int *k2, |
| const mp_int *px, const mp_int *py, mp_int *rx, mp_int *ry) |
| { |
| mp_err res = MP_OKAY; |
| mp_int k1t, k2t; |
| const mp_int *k1p, *k2p; |
| |
| MP_DIGITS(&k1t) = 0; |
| MP_DIGITS(&k2t) = 0; |
| |
| ARGCHK(group != NULL, MP_BADARG); |
| |
| /* want scalar to be less than or equal to group order */ |
| if (k1 != NULL) { |
| if (mp_cmp(k1, &group->order) >= 0) { |
| MP_CHECKOK(mp_init(&k1t)); |
| MP_CHECKOK(mp_mod(k1, &group->order, &k1t)); |
| k1p = &k1t; |
| } else { |
| k1p = k1; |
| } |
| } else { |
| k1p = k1; |
| } |
| if (k2 != NULL) { |
| if (mp_cmp(k2, &group->order) >= 0) { |
| MP_CHECKOK(mp_init(&k2t)); |
| MP_CHECKOK(mp_mod(k2, &group->order, &k2t)); |
| k2p = &k2t; |
| } else { |
| k2p = k2; |
| } |
| } else { |
| k2p = k2; |
| } |
| |
| /* if points_mul is defined, then use it */ |
| if (group->points_mul) { |
| res = group->points_mul(k1p, k2p, px, py, rx, ry, group); |
| } else { |
| res = ec_pts_mul_simul_w2(k1p, k2p, px, py, rx, ry, group); |
| } |
| |
| CLEANUP: |
| mp_clear(&k1t); |
| mp_clear(&k2t); |
| return res; |
| } |
